Editing Pick's theorem (section)

==Related topics==
Several other mathematical topics relate the areas of regions to the numbers of grid points. [[Blichfeldt's theorem]] states that every shape can be translated to contain at least its area in grid points.{{r|olds}} The [[Gauss circle problem]] concerns bounding the error between the areas and numbers of grid points in circles.{{r|guy}} The problem of counting [[integer points in convex polyhedra]] arises in several areas of mathematics and computer science.{{r|barvinok}}
In application areas, the [[dot planimeter]] is a transparency-based device for estimating the area of a shape by counting the grid points that it contains.{{r|bellhouse}} The [[Farey sequence]] is an ordered sequence of rational numbers with bounded denominators whose analysis involves Pick's theorem.{{r|bruarc}}

Another simple method for calculating the area of a polygon is the [[shoelace formula]]. It gives the area of any simple polygon as a sum of terms computed from the coordinates of consecutive pairs of its vertices. Unlike Pick's theorem, the shoelace formula does not require the vertices to have integer coordinates.{{r|braden}}